The Magpies, who travel to fellow strugglers Hull City on Saturday, have endured a traumatic campaign and are only separated from the relegation zone by goal difference.
To make matters worse for Newcastle, they have played a game more than 18th-placed Portsmouth and face, arguably, the toughest run-in of all the clubs in the bottom half of the division.
With UEFA Champions League quarter-finalists Arsenal and Chelsea to visit St James' Park and a trip to Aston Villa lurking on the final day, Gutierrez is eager to get points on the board sooner rather than later.
DangerHe said: "The aim is to be safe before the end of the season.
"We are trying to avoid going into the last home game or away game when we need to win to stay up.
"Now we have to take three points from Hull and start a run that will take us away from danger.
"I try not to think about the relegation zone. I think we will get out of the fight at the bottom.
Nervous"All we need to do is win against Hull and move up the table.
"The feeling at the moment I have is not a nervous one - we want to play Hull straight away.
"Bring it on - that is the feeling ahead of this match.
"We know that this game is very important to us and what it means for us between now and the end of the season."